No it’s not. It’s just like how someone would say
▪️The boys use proper grammar
Or
▪️I use proper grammar
Not
◾️Me uses proper grammar.
I do, however, see your point. The meme is a fragment because this guy uses the infinitive of use instead of the actual verb. It should have said “use” or “Using proper grammar with the boys is cool” or “The boys and I are using proper grammar.”